Express the following percentages as decimals and fractions.
i. `15%` ii. `8(1)/(3)%` iii. `120%` iv. `33(1)/(3)%`

Answer

Let's solve the problem step by step.

### Question: Express the following percentages as decimals and fractions.
1. **15%**
2. **8(1)/(3)%**
3. **120%**
4. **33(1)/(3)%**

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### Step 1: Convert 15% to Decimal and Fraction

**Fraction:**
- To convert 15% to a fraction, we write it as:
\[ \frac{15}{100} \]
- Now, simplify the fraction:
\[ \frac{15 \div 5}{100 \div 5} = \frac{3}{20} \]

**Decimal:**
- To convert 15% to a decimal, we divide by 100:
\[ 15 \div 100 = 0.15 \]

### Step 2: Convert 8(1)/(3)% to Decimal and Fraction

**Fraction:**
- First, convert \(8(1/3)\) to an improper fraction:
\[ 8 \frac{1}{3} = \frac{25}{3} \]
- Now, convert it to a fraction:
\[ \frac{25}{3} \div 100 = \frac{25}{300} = \frac{1}{12} \quad \text{(after simplification)} \]

**Decimal:**
- To convert \(8(1/3)\)% to decimal:
\[ \frac{25}{3} \div 100 = \frac{25}{300} = 0.0833 \quad \text{(approximately)} \]

### Step 3: Convert 120% to Decimal and Fraction

**Fraction:**
- To convert 120% to a fraction, we write it as:
\[ \frac{120}{100} \]
- Now, simplify the fraction:
\[ \frac{120 \div 20}{100 \div 20} = \frac{6}{5} \]

**Decimal:**
- To convert 120% to a decimal:
\[ 120 \div 100 = 1.2 \]

### Step 4: Convert 33(1)/(3)% to Decimal and Fraction

**Fraction:**
- First, convert \(33(1/3)\) to an improper fraction:
\[ 33 \frac{1}{3} = \frac{100}{3} \]
- Now, convert it to a fraction:
\[ \frac{100}{3} \div 100 = \frac{100}{300} = \frac{1}{3} \quad \text{(after simplification)} \]

**Decimal:**
- To convert \(33(1/3)\)% to decimal:
\[ \frac{100}{3} \div 100 = \frac{100}{300} = 0.333 \quad \text{(approximately)} \]

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### Summary of Answers:
1. **15%** = \( \frac{3}{20} \) and \( 0.15 \)
2. **8(1)/(3)%** = \( \frac{1}{12} \) and \( 0.0833 \)
3. **120%** = \( \frac{6}{5} \) and \( 1.2 \)
4. **33(1)/(3)%** = \( \frac{1}{3} \) and \( 0.333 \)

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